The measurement and management of the downside risk of portfolios is a key issue for financial institutions. The industry standard Value at Risk (VaR) shows serious deficiencies as a measure of the downside risk. It penalizes diversification in many situations and does not take into account the size of very large losses exceeding the value at risk. These problems motivated intense research on alternative static and dynamic risk measures.
While axiomatic results are an important first step towards better risk management, an analysis of the economic implications of different approaches to risk management should not be neglected. Risk limits influence the behavior of economic agents – and this impact is not captured by the classical analysis. The talk will discuss recent research on portfolio choice under risk constraints.